find the area of the circle shown. the diameter is given.

11. Dimension of Row Space = 3.

12. Dimension of Row Space = 1.

13. largest possible rank is 5.

14. largest possible dimension is 3.

15. Dimension of Nul A = 2.

Let's discuss it further below.

11. The dimension of the row space of an 8x5 matrix A can be found using the Rank-Nullity theorem, which states that the rank of a matrix (dimension of the row space) plus the dimension of the null space equals the number of columns in the matrix. So, if the null space is 2-dimensional, then the dimension of the row space is:

Dimension of Row Space = 5 (number of columns) - 2 (dimension of null space) = 3.

12. For a 5x6 matrix A, the Rank-Nullity theorem can also be applied. If the null space is 4-dimensional, then the dimension of the row space is:

Dimension of Row Space = 5 (number of rows) - 4 (dimension of null space) = 1.

13. The largest possible rank of a 7x5 matrix A is equal to the minimum of the number of rows and columns, which in this case is 5. For a 5x7 matrix A, the largest possible rank is also the minimum of the number of rows and columns, which is 5.

14. The largest possible dimension of the row space of a 4x3 matrix A is the minimum of the number of rows and columns, which is 3. For a 3x4 matrix A, the largest possible dimension of the row space is also the minimum of the number of rows and columns, which is 3.

15. The smallest possible dimension of Nul A for a 6x8 matrix can be found using the Rank-Nullity theorem. The largest possible rank of a 6x8 matrix A is the minimum of the number of rows and columns, which is 6. Thus, the smallest possible dimension of Nul A is:

Dimension of Nul A = 8 (number of columns) - 6 (largest possible rank) = 2.

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Answer:

10002

Step-by-step explanation: I think this is correct

Answer:

10002

Step-by-step explanation:

9,857 + 310 ÷ 2 - 10 = 10002

The increase in weekly wages for both the man and the boy is Rs. 40.

Let's assume that the increase in wages for both the man and the boy is x.

After the increase, the man's weekly wage will be Rs. 80 + x and the boy's weekly wage will be Rs. 35 + x.

We know that the man's wage after the increase is 8/5 of the boy's wage after the increase. Mathematically,

80 + x = (8/5)(35 + x)

Simplifying this equation, we get:

80 + x = 56 + (8/5)x

Multiplying both sides by 5, we get:

400 + 5x = 280 + 8x

Subtracting 5x from both sides, we get:

400 = 280 + 3x

Subtracting 280 from both sides, we get:

120 = 3x

Dividing both sides by 3, we get:

x = 40

Therefore, the increase in wages is Rs. 40.

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Answer:

Step-by-step explanation:

Answer: Where is the image?

Step-by-step explanation:

If the number b is 90% less than 47 and the number a is 110% greater than b, then the value of a is 9.87.

If the number b is 90% less than 47, that means b is equal to 10% of 47, which can be calculated as:

b = 0.1 x 47

b = 4.7

If the number a is 110% greater than b, that means a is equal to 100% (or 1) plus 110% (or 1.1) of b, which can be calculated as:

a = (1 + 1.1) x b

a = 2.1 x 4.7

a = 9.87

Therefore, the value of a is 9.87.

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Answer:

The Position Vectors of points A,B,C with respect to the origin are 8i-10j, 2i+6j and -10i +4j respectively. If ABCN is a parallelogram find The Position Vector of N. /AN/ and /AB/. Acute angle between AN and AB

Answer:

Let the length of the rectangle be x and the width of the rectangle be y.

Then, we can use the Pythagorean Theorem to find the value of x and y:

x2 + y2 = 62

x2 + y2 = 36

We can use trigonometry to find the value of x and y:

x = 6 sin 30°

y = 6 cos 30°

Therefore, the length of the rectangle is 6 sin 30° cm and the width of the rectangle is 6 cos 30° cm.

Step-by-step explanation:

First of all

You should draw a straight line which is AC=6cm

Then you should take the centre of the line and draw

30 degree in centre. Then you should draw straight line from

30 degree to bisect center point. Then take 3 cm in compass

and join their point.

The approximate distance between Khloe and school is given by 18.78 miles.

Representing Khloe's movements on a coordinate plane.

Let us assume that Khloe's starting point (her school) is at the origin (0,0).

She walks 20 miles due west,

which means she moves 20 units to the left on the x-axis. Her new position is (-20,0).

She then walks 8 miles due north,

which means she moves 8 units up on the y-axis.

Her new position is (-20,8).

Finally, she walks 3 miles due east,

which means she moves 3 units to the right on the x-axis.

Her new position is (-17,8).

Distance between Khloe's final position and her starting point (the school),

Use the Pythagorean theorem,

Distance = √((change in x)^2 + (change in y)^2)

⇒Distance = √((-17-0)^2 + (8-0)^2)

⇒Distance = √(289 + 64)

⇒Distance = √353

⇒Distance ≈ 18.78 miles

Therefore, Khloe is approximately 18.78 miles away from her school.

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Answer : n⁸

:) ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍

well actually, your answer is -2

not positive 2

you have to take the 9, and subtract it from the other side (the -15), giving you -24

then you divide -24 by 12, giving you x=-2

this is true because when you plug it back in, you get 12 x -2 = -24

-24 + 9 = -15

The probability that in a random sample of 190 Americans aged 14 or older, more than 27 are single is approximately 0.9975

To solve this problem, we can use the normal approximation to the binomial distribution.

First, we need to calculate the mean and standard deviation of the number of singles in a sample of 190 Americans aged 14 or older.

Mean

μ = n × p = 190 × 0.22 = 41.8

Standard deviation

σ = sqrt(n ×p × (1 - p)) = sqrt(190 × 0.22 × (1 - 0.22)) = 5.27

Now, we can use the standard normal distribution to calculate the probability that more than 27 people in the sample are single. We convert the binomial distribution to a normal distribution by using the following formula

z = (x - μ) / σ

where x is the number of singles in the sample.

z = (27 - 41.8) / 5.27 = -2.80

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of -2.80 or lower is approximately 0.0025.

However, we want to find the probability of getting more than 27 singles, so we need to find the area to the right of z = -2.80. This is equivalent to subtracting the probability of getting a z-score of -2.80 or lower from 1:

P(Z > -2.80) = 1 - 0.0025 = 0.9975

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Answer:

121,68

Step-by-step explanation:

First we need to find how smaller the new number will be:

[tex] \frac{144 \times 15.5\%}{100\%} = 22.32[/tex]

Then we subtract this number from 144:

144 - 22,32 = 121,68

And there we have the answer

The percentage of all possible values of the variable that lie between 10 and 16 is 97.71%, the percentage of all possible values of the variable that are at least 18 is 0.01% and the percentage of all possible values of the variable that are at most 8 is 0.01%.

Given that, variable is normally distributed with mean and standard deviation .

To find the percentage of all possible values of the variable that lie between and .

We can convert the given variable to standard normal variable using Z= (X- μ )/ σ

Therefore, we get, Z1 = (10- 12)/ 1 = -2 And Z2 = (16-12)/1 = 4

Thus, the probability of values that lie between 10 and 16 is given by

P(-2 ≤ Z ≤ 4) = P(Z ≤ 4) - P(Z ≤ -2) = 0.9999 - 0.0228 = 0.9771 = 97.71%.b)

To find the percentage of all possible values of the variable that are at least .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,

Z = (18-12)/1 = 6

The probability of values that are at least 18 is given by

P(Z ≥ 6) = 1- P(Z ≤ 6) = 1- 0.9999 = 0.0001 = 0.01%.c)

To find the percentage of all possible values of the variable that are at most .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,

Z = (8-12)/1 = -4

The probability of values that are at most 8 is given byP(Z ≤ -4) = 0.0001 = 0.01%.

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The rate of 50 deaths per 1,000 births is known as the infant mortality rate.

What is infant mortality rate?

Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age. Infant mortality rate is an essential demographic statistic for assessing population health status and identifying health disparities among different groups of the population.

IMR reflects the underlying mortality rate of infants in a society, which can be influenced by several factors, including maternal health, access to healthcare, nutrition, and socio-economic factors.Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age.

The rate of 50 deaths per 1,000 births is known as the infant mortality rate. The infant mortality rate is considered one of the most critical indicators of a country's health status and is often used to compare the health status of different populations.

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It seems that the table has not been provided in the question. However, I can provide a general method to complete the table based on the given information.

If each rectangle is 16% longer than the original, we can calculate the length of each new rectangle by adding 16% of the original length to the original length.

Let L be the original length of the rectangle. Then, the length of the new rectangle would be L + 0.16L = 1.16L.

Using this formula, we can calculate the length of the new rectangle for any given original length. For example, if the original length is 10 cm, then the length of the new rectangle would be:

1.16 x 10 cm = 11.6 cm

Similarly, we can calculate the length of the new rectangle for any other original length and complete the table accordingly.

The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.

The line of best fit for this data is y = 5.3x + 23. This equation can be used to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes. To calculate this, substitute x = 6 into the equation: y = 5.3(6) + 23. Simplifying this equation, we get y = 31.8 + 23, which gives us y = 54.8. This is the temperature of the water in the beaker if heated for 6 minutes, which is approximately 91.8°C. hence, The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.

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Answer: Answer is below <3

Step-by-step explanation:

1. —1x²(3x²—7x—5)
2. 14x ² (y²—2x+4x²)

3. 8100m²y4

4. (a5— 7b6) (a5 — 7b6)

5. (m+1) (m+11)

6. (a+1) (a+6)

7. —3x+6

8. (—6a+1) (—6a+1) / 4

9. (x+5)²

10. X² — 7xy—88x

Hope this helps!

Then we can fill out the table of joint relative frequency as follows:

               Small        Large

Male         5/50        18/50

Female    21/50        6/50

Joint relative frequency is a statistical term that refers to the proportion of individuals in a population that share two or more specific characteristics. In other words, it measures the frequency or occurrence of a specific combination of two or more variables within a larger population.

Here,

To find the joint relative frequencies, we need to divide each cell by the total number of people (males + females).

Here, we added up the number of males and females to get the total number of people (50). Then, we divided the number of males who ordered a small sandwich (5) by 50 to get the relative frequency of males who ordered a small sandwich (5/50), and so on for each cell in the table.

To calculate the joint relative frequencies, we need to divide each cell in the second table by the total number of observations, which is the sum of all cells in the first table.

The total number of observations is:

5 + 18 + 21 + 6 = 50

To calculate the joint relative frequency for the first cell (small sandwich, male), we divide the number of observations in that cell by the total number of observations:

joint relative frequency = 5/50 = 0.1

Note that the sum of the relative frequencies in each column should add up to 1, since we are dividing by the total number of people.

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Answer:

$3.75b + $25 >= $1100

Step-by-step explanation:

The trig ratios as fractions expressed in simplest terms is :cos(K) = 8 √(17)/17  , sin(L) = 9 √(17)/17

Trigonometric ratios are mathematical relationships between the angles and sides of a right-angled triangle. They are ratios of the lengths of two sides of a right triangle in relation to one of its acute angles. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly denoted as sin, cos, and tan, respectively.

Sine: The sine of a right triangle angle seems to be the ratio of the length of the opposite side towards the length of the hypotenuse.

Cosine: The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the angle towards the length of the hypotenuse.

Tangent: In a right triangle, the tangent of an angle is really the ratio of the length of the side opposite the angle to the length of the adjacent side.

Given: A right angle triangle JKL, with angle J = 90 degrees, JL = sqrt(17), JK = 8, LK = 9

We can use the following trigonometric ratios:

To find the values of sin(L) and cos(K), we need to identify the opposite, adjacent and hypotenuse sides of the angles L and K.

For angle K:

cos(K) = adjacent/hypotenuse = JK/JL = 8/√(17)

To make the fraction easier to understand, multiply the numerator and denominator by √(17):

cos(K) = (8/√(17)) x (√(17)/√(17)) = (8 √(17))/17

Therefore, cos(K) = 8 √(17)/17

For angle L:

sin(L) = opposite/hypotenuse = LK/JL = 9/√(17)

To make the fraction easier to understand, multiply the numerator and denominator by √(17):

sin(L) = (9/√(17)) x (√(17)/√(17)) = (9 √(17))/17

Therefore, sin(L) = 9 √(17)/17

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

c

Step-by-step explanation:

Answer:

The Distributed Pattern Matching (DPM) problem have provided mathematical analysis and simulation results for establishing the effectiveness of the proposed architecture. DPMS achieves many desirable properties of both the unstructured and structured P2P systems. Like unstructured systems DPMS supports partial keyword matching, utilizes the heterogeneity in peer capabilities, and does not place any hard restriction on index/document placement. Like structured systems, on the other hand, DPMS attains logarithmic bound on search complexity and offers guarantee on search completeness and discovery of rare items. Advertisement traffic in DPMS is comparable to that of DHT-based structured P2P systems. To our knowledge Distributed Pattern Matching (DPM) problem has never been addressed by any research activity in P2P context. 1 The index distribution architecture of DPMS is unique and has been designed specifically to solve the DPM problem. The novel aggregation scheme, proposed in this paper, can effectively reduce storage overhead at the indexing peers without incurring a significant decrease in query routing performance. However, the use of bloom filter for representing indices is not new. Many network applications use bloom filters. A comprehensive list of such applications can be found in [6]. The rest of this paper is organized as follows. Section II highlights and compares the approaches related to DPMS. The architecture and operation of DPMS are presented in section III. Mathematical analysis of search complexity in DPMS is provided in section IV.

Answer: 6 bricks long by 6 bricks wide

Step-by-step explanation:

Since her first arrangement is a 12 x 3 brick patio, we can assume she has 36 bricks. A square has equal lengths of all sides, with this info, she can arrange the 36 bricks into a 6 by 6 patio

Answer:

top left and top right

Step-by-step explanation:

a right angle is 90⁰

The specified details of the triangle, obtained using the segments joining the midpoints of the sides of the triangle ΔADG and trapezoid ACFG indicates that we get;

4. [tex]\overline{CE}[/tex] is a midsegment of ΔBDF

[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG

5. CE = 12 cm, AG = 36 cm

6. m∠2 = 116°, m∠3 = 32°, m∠4 = 58°, m∠5 = 58°, m∠6 = 64°

The midpoint of a segment or the side of a triangle is a point that divides the segment into two parts of the same length.

4. The details of the diagram indicates that the segment [tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF

[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG

5. [tex]\overline{CD}[/tex] is congruent to [tex]\overline{BC}[/tex] by the definition of the midpoint of [tex]\overline{BD}[/tex], similarly;

[tex]\overline{BC}[/tex] is congruent to [tex]\overline{AB}[/tex], by the definition of midpoint of [tex]\overline{AC}[/tex], therefore;

[tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF, therefore;

CE = (1/2) × BF

CE = (1/2) × 24 cm = 12 cm

CE = 12 cm

ΔBDF and ΔADG and ΔCDE are similar triangles, therefore;

[tex]\overline{BD}[/tex] = (2/3) × [tex]\overline{AD}[/tex]

Similarly, by the relationship between similar triangles we get;

[tex]\overline{BF}[/tex] = (2/3) × [tex]\overline{AG}[/tex]

BF = 24 cm, therefore;

24 = (2/3) × AG

AG = (3/2) × 24 = 36

AG = 36 cm

6. The length of a median of a right triangle, drawn from the right angled vertex, is half the length of the hypotenuse side.

Therefore; ΔACM and ΔABM are an isosceles triangles

m∠1 = m∠3 = 32°

m∠2 = 180° - (32° + 32°) = 116°

m∠2 = 116°

m∠3 = 32°

m∠4 = m∠5 = 90° - m∠1

m∠4 = m∠5 = 90° - 32° = 58°

m∠4 = 58°

m∠5 = 58°

m∠6 = 180° - (m∠4 + m∠5)

m∠6 = 180° - (58° + 58°) = 64°

m∠6 = 64°

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